Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#65363 |
| Fitting | C3×C5×#127 ⋊ C2 |
| Hall | C3×C5 ⋊ #496 |
| Sylow | C5 ⋊ C3×#496 |
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(4,5,7,8,6)(10,12)(14,18)(15,20)(17,19);(9,10,11,12)(14,17)(18,19);(5,6)(7,8)(10,12)(13,14)(15,18)(16,17)(19,20)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598748, #14279396, C3×#10602119, … |
| maximal normal subgroup of | C3×#10598748, #14279396, C3×#10602119, … |
| maximal quotient of | C3×#10602050, C3×#10602052, C3×#10602053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4166);